Resistivity logging tools have been used for many years to measure the resistivity of formations surrounding a borehole.
In a typical resistivity measuring tool a pair of receivers is located between two transmitters. The transmitters when excited with a sinusoidal current, induce a voltage in the loops formed by the drill collar and the formation. This voltage, which can be measured by a secondary winding, creates a current in the formation and the borehole mud. A receiver measures the current running on the drill collar at the location of the receiver. A pair of receivers can measure the difference in axial current, which is the radial current entering the formation between the two receivers.
A transmitter-receiver pair measures the conductance of the formation along the current loop established. This conductance is (except for frequency effects) inversely proportional to the formation resistivity. An example of this method is a bit resistivity measurement. If a pair of receivers is used and the difference in axial currents is measured, the resistivity derived is dominated by the formation in front of the space between the two receivers. Combining two such measurements, with a transmitter above and another below the receiver pairs, allows focusing more precisely the current into the formation and obtaining a more precise resistivity measurement.
U.S. Pat. No. 3,305,771 discloses a logging-while-drilling system using a pair of spaced-apart transmitting toroidal coils and a pair of spaced-apart receiving toroidal coils between the transmitting toroidal coils. An alternating current generator excites the toroidal transmitters, which induces current into the formation. The receivers detect the current that passes out of the collar into the formation between the two receivers.